Sotnikov A. First-principle and mean-field theoretical approaches to the description of near-critical phenomena in quantum gases

The Doctoral Thesis presents the results of the research on the near-critical phe-nomena in quantum gases by means of the first-principle and mean-field theoretical approaches. In particular, thermodynamic characteristics of ideal gases in the regime of quantum degeneracy are studied on the whole temperature range including those intervals, where the perturbation-theory expansions become inaccurate. Effects of filtering of optical pulses by ultracold gases of alkali atoms are studied and a principal possibility of acceleration of relativistic charged particles in these systems in the state with a Bose-Einstein condensate are shown. The dynamical mean-field theoretical approach is generalized for the cases of interacting Fermi-gases with different tunneling amplitudes, particle densities, high spin symmetries and the presence of the Hund-type exchange terms. For ultracold gases of Fermi-atoms in optical lattices, phase diagrams with magnetic phases are obtained and effective spin models in the strong-coupling limits are derived. The Bose-condensation phenomenon of spin-triplet excitons in cobalt oxide crystals is predicted and hysteresis behavior in external strong magnetic field is explained. Low-temperature phase diagrams of the cobalt-oxide crystals doped by lanthanum-group elements, calcium, strontium, and fluorine are studied. Dispersive characteristics of the excitations in these systems are analyzed and it is shown that the results of the developed theoretical approaches agree well with the experiments performed with the resonant inelastic X-ray scattering.